Multi-Group Analysis in AMOS The Mediation Model Across a Moderator

22 Pages·2015·0.33 MB·English

Multi-Group Analysis in AMOS
(with pairwise tests of path coefficients)
Synopsis: The following notes contain procedures on how to do a multi-
group analysis in AMOS, and how to instruct AMOS to test for pairwise
path coefficient differences. Please note that what follows is just an
example of how this can be done, and since we're using such a small
sample size, p-values are not computed for the chi-squared test. In
practice, you would be using a much larger sample size, and would have
more degrees of freedom. What follows is only for demonstration
purposes.
The Mediation Model Across a Moderator
If we consider the classic 3-variable mediation model (Baron & Kenny,
1986), there are times when we may be interested in knowing whether the
mediation model holds across levels of a moderator, where the levels of
the moderator represents distinct, mutually exclusive and independent
groups. Consider the following example in which we have a mediation
model across 5 levels of a moderator:
Y - dependent variable
X - independent variable
M - mediator
Z - moderator (categorical, 5 levels)
The questions that arise from the above include the following:
1. Is path "a" for Z = 1 statistically different from path "a" for Z =
2? Is path "a" for Z = 1 statistically different from path "a" for Z =
3? Etc., for other pairwise comparisons of paths "a" across levels of
Z.
2. Is path "b" for Z = 1 statistically different from path "b" for Z =
2? Is path "b" for Z = 1 statistically different from path "b" for Z =
3? Etc., for other pairwise comparisons of paths "b" across levels of
Z.
3. Is path "c" for Z = 1 statistically different from path "c" for Z =
2? Is path "c" for Z = 1 statistically different from path "c" for Z =
3? Etc., for other pairwise comparisons of paths "c" across levels of
Z.

Example Using a Categorical Moderator with Two Groups

In the following example, we consider the case of only two groups,
though the example can be generalized to situations in which you have
more than 2 groups, such as in the example given above in the
introduction to these notes.

Consider the situation in which you are interested in knowing whether a
path model is consistent across 2 groups. In this example, we consider
a basic 3-variable mediational model, then ask the question of whether
the model is consistent across 2 groups. The 2 groups are actual levels
of a "moderator," so what we are actually testing is related to what is
generally called moderated mediation. That is, we are comparing the
mediational model across levels of Z, and wanting to conclude whether
the mediation is moderated by levels of Z, and if so, which paths in
the 3-variable model are different from which others.

For the 3-variable path models noted above, the test of the equality of
the "a" parameters is a test of mediated moderation (which we do not
discuss further in these notes). The test of the equality of the "b"
parameter is a test of moderated mediation (Baron & Kenny, 1986;
MacKinnon, 2008), and is the technique we do discuss in these notes.

Let's draw up some fictional data in SPSS to perform these analyses.
Note that we will be using an extremely small sample size, and that
usually, you would want a much larger sample size to conduct path
analysis or SEM analysis more generally.

As previously done, but this time having a moderator with only 2
levels, we define the following:

Y - dependent variable
X - independent variable
M - mediator
Z - moderator (categorical, 2 levels)

Here's what our fictional data look like when entered into SPSS:
Notice that we have 20 cases in total, Y, X, and M are all continuous
variables, and Z (our moderator) is dichotomously scored. What we want
to test is whether the mediation model of "X predicts Z through M" is
consistant across our two levels of Z. We also want to do pairwise
comparisons of paths across the two groups, to be able to pinpoint path
differences.

Procedures in AMOS
Start up AMOS Graphics, and draw the simplest mediation model:

We now tell AMOS that the above will represent a path diagram for two
distinct groups (recall that we're using two groups in our example, you
may have more in your data). To do this, click on "Analyze," then
"Manage Groups":
Notice by default AMOS identifies the first group as "Group 1." You can
keep this name for group 1, or you can select a different name. For
instance, suppose your first group represents "Bullies" and the second
group represents "Victims." You would enter "Bullies" for group 1, and
"Victims" for group 2. For now, we'll just call our two groups "Group
1" and "Group 2." So, we leave the text above as is, and select "New"
to enter our second group as follows:

Once you're done entering your groups, you can close the "Manage
Groups" window. When you return to the main AMOS window, your groups
will appear on the interface (double-check to make sure they are
there):

Next, tell AMOS which data file to use. Since for this example we saved
our SPSS data file as "group_data," we'll tell AMOS to fetch this file
for use with the present analysis. We will have to instruct it to use
the file for BOTH groups, since we stored the data in one data file.
There are times in which you may have two data files (each file
containing a different group of objects), which would call for slightly
different procedures. For now, however, we only have the one data file.
Click under "File" then "Data Files" to open the data file window:
The above requires some explanation. To obtain the above, we first
selected "Group 1" then clicked on "File Name" and selected the SPSS
data file (it's the only data file we're using, we don't have separate
data files for each group). Once the file for group 1 is selected,
click on "Grouping Variable," and it will bring up the following
window:

Since our grouping variable is variable Z, we select "Z" and then "Ok."
Next, click on "Group Value" from the "Data Files" window. It will
bring up the following window:
The function of the above screen is simply to verify that your groups
are coded correctly. Check the above screen to make sure all is in
order. In our SPSS data file, we coded group 1 as "0" and group 2 as
"1" so all looks good above. We see as well that there are 10
observations per group (Freq = 10, 10).

Next, select "Group 2" from the main window. Repeat the above steps and
select the same data file as for Group 1 (since recall, all of our data
is in one file). Your final "Data Files" window, if you've done
everything correctly, should look as follows:
Notice that we have identified two groups above, with both "Group 1"
and "Group 2" taking its data from "group_data.sav." We've identified
the grouping variable to be "Z", and the value of each group is "0" and
"1". The total N per group is 10 out of 20 objects. Click "Ok" and
we're ready to move on.

Naming Paths in the Mediational Model
We now have to name the paths "a" "b" and "c" distinctly for each
group. First however, we need to complete our model by adding residual
terms to "M" and "Y" (we name them "r1" and "r2" below):

Recall why we're adding the residual terms above. Both "M" and "Y" are
endogenous variables, meaning that they are being predicted by other
variables in the model. "X" doesn't have a residual term because it
isn't being predicted by anything. The drawing of the model is now
complete.

The next steps are very crucial to making sure we're able to obtain the
pairwise comparisons of coefficients. In the AMOS tab that displays the
groups,

choose "Group 2" and then right-click on the path from X to M in the
path diagram. Select "Object Properties," then "Parameters." Under
"Regression Weight," call the path by the name of a2 (to identify this
path as the path "a" for group 2 and DESELECT "All groups." Notice in
the following that "Regression weight" is identified as "a2" and we've
deselected "All groups":
When you close this window, the path "a2" should appear in the path
diagram (as it does in the following):

Repeat the above process for paths "b" (from M to Y) and "c" (from X to
Y), being sure to "deselect" the "All groups" box for all paths, so
that you obtain the following picture:

Model 2 (i.e., "Model 2" is "Group 2's" model) is now ready. To prepare
Model 1, select "Group 1" and do the same as was done for Model 2, but
this time, identify all the paths as simply "a" "b" "c". As was done
for Model 2, deselect "All groups" for each path. You should have a
path diagram for Model 1 that looks like the following:

Reviewing The Two Models
Let's take a moment to review what we've done so far. If everything was
done correctly, you should now have two models drawn in AMOS that you
are going to run. They won't both be on the same screen, but rather
they will be selected by choosing "Group 1" or "Group 2" from the AMOS
interface. They should look like this - Model 1 is on the left, and
Model 2 is on the right:

How to Tell AMOS to do Pairwise Comparisons of Coefficients

Recall that what we would like to do is, in addition to comparing the
fit of the two models, compare coefficients a1 to a2, b1 to b2, c1 to
c2, etc. These pairwise comparisons (among others) will be produced
when we run the analysis. To instruct AMOS to compare all paths within
and between the two models, select "View" then "Analysis Properties."
The following window will appear:

Select "Output" in the top panel: